Among the variety of antenna assemblies that have been proposed for airborne and spaceborne applications are those unfurlable structures which employ an inflatable membrane or laminate to form a `stressed skin` type of reflective surface. In the configurations which have been proposed to date, non-limiting examples of which are described in U.S. Pat. Nos. 4,364,053 and 4,755,819, the surface of the inflatable structure itself serves as the reflective surface of the antenna. Namely, the inflatable material has a preformed geometry, so that, once fully inflated, its surface will assume the desired antenna geometry. A significant drawback to such structures, however, is the fact that should there be a change in inflation pressure, most notably a decrease in pressure over time, the contour of the support structure and therefore that of the reflective surface itself, will change from the intended antenna profile, thereby impairing the energy gathering and focussing properties of the antenna.